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Polynomial: a mathematical expression

by Dawn
(Sebring, Ohio)










































Polynomial Expressions

Polynomials are algebraic expressions which are the sum of monomials.

     • Is the following a polynomial ?

         -5x +1/(6x)

   If so,

     • How many terms and variables are there?

     • What degree is it?

Comments for Polynomial: a mathematical expression

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Sep 08, 2012
What is a Polynomial?
by: Staff

Answer:
Part I

What is a polynomial?

     • In mathematics, the term POLYNOMIAL refers to an algebraic expression which is (only) the SUM, DIFFERENCE, or MULTIPLICATION of individual TERMS.

          The following algebraic expressions are EXAMPLES of POLYNOMIALS.

          All four expressions shown are the sum, difference, or multiplication of individual terms.

              3                    [terms: 3]

              3x³                 [terms: 3x³]

              3x³ + x² - 3                     [terms: 3x³, x², -3]

              (3x³ + x² - 3) * (4x)          [terms: 3x³, x², -3]

          However, there are RESTRICTIONS on what kind of TERMS can be used in a polynomial.

          Only terms which have exponents which are positive integers and terms which are not divided by a variable can be used to form polynomial expressions.

          The following are examples of TERMS which CAN BE USED to form a polynomial:

              3x³, term                (VALID term for polynomial)

              4x, term                 (VALID term for polynomial)

              ax², term                (VALID term for polynomial)

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Sep 08, 2012
What is a Polynomial?
by: Staff

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Part II

              (1+i)x³, term           (VALID term for polynomial; 1+i is a complex number)

              sqrt(3), term           (VALID term for polynomial; sqrt(3) is a constant)


          The following are examples of TERMS which CANNOT BE USED to form a polynomial:


              1/t, term           (NOT valid term for polynomial: the variable is in the denominator. 1/t = t⁻¹, a negative exponent)

              x⁻⁷, term          (NOT valid term for polynomial: negative exponent)

              y¾, term          (NOT valid term for polynomial: fractional exponent)

              sqrt(x), term     (NOT valid term for polynomial: sqrt = fractional exponent of ½)


Is the following a polynomial ?

     -5x +1/(6x)

     NO, it is NOT a POLYNOMIAL. 1/(6x) is not a valid term because it contains a division by the variable “x”.

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Sep 08, 2012
What is a Polynomial?
by: Staff


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Part III


Here is a little more information which may be helpful:

          Polynomials are often classified by the number of terms they have, or by degree.

             Polynomial classification by the number of terms:

                 Monomials are polynomials with one term (e.g.: x).

                 Binomials are polynomials with two terms (e.g.: x² + x).

                 Trinomials are polynomials with three terms (e.g.: x² + x + 5) .

                 Quadrinomials are polynomials with four terms (e.g.: 2x³ - x² + x + 5)

                 When polynomials have more than four terms they are just called polynomials.



             Polynomial classification by highest exponent:

                 Constant (eg: 3)

                 Linear (eg: y + 6)

                 Quadratic (eg: x² + 6)

                 Cubic (eg: x³ + 6)

             You can also combine the names:


                 Quadratic Binomial (eg: x² + 6)

                 Cubic Trinomial (eg: 2x³ - x² + x)

                 Etc.



Thanks for writing.

Staff
www.solving-math-problems.com



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